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Theorem jctl 307
Description: Inference conjoining a theorem to the left of a consequent. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Wolf Lammen, 24-Oct-2012.)
Hypothesis
Ref Expression
jctl.1 𝜓
Assertion
Ref Expression
jctl (𝜑 → (𝜓𝜑))

Proof of Theorem jctl
StepHypRef Expression
1 id 19 . 2 (𝜑𝜑)
2 jctl.1 . 2 𝜓
31, 2jctil 305 1 (𝜑 → (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106
This theorem is referenced by:  mpanl1  425  mpanlr1  431  reg2exmidlema  4350  relop  4586  nn0n0n1ge2  8817  expge1  9992  4dvdseven  11195  ndvdsp1  11210
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