Consequential conditionals are defined as "if P then Q" statements, where P is an action, and Q a predicted outcome of this action, which is either desirable or undesirable to the agent. Experiment 1 shows that desirable (viz. undesirable) outcomes invite an inference to the truth (viz. falsity) of their antecedent. Experiment 2 shows that the more extreme the outcome is, the stronger the invited inference is. Experiment 3 shows that modus ponens from premises "If A then C, A" can be suppressed with the introduction of a consequential conditional, "If C then Q," where Q is an undesirable outcome. Experiment 4 shows that the more undesirable Q is, the larger the suppression is. The authors discuss how these results can enrich current approaches of conditional inference on the basis of mental models, complementary necessary conditions, and conditional probabilities.